Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1288,2,Mod(1,1288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1288, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1288.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1288 = 2^{3} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1288.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(10.2847317803\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.27841\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1288.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.27841 | 0.738092 | 0.369046 | − | 0.929411i | \(-0.379684\pi\) | ||||
0.369046 | + | 0.929411i | \(0.379684\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.477194 | −0.213408 | −0.106704 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106704 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.36566 | −0.455220 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.43556 | −0.734349 | −0.367175 | − | 0.930152i | \(-0.619675\pi\) | ||||
−0.367175 | + | 0.930152i | \(0.619675\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.18356 | −1.99236 | −0.996180 | − | 0.0873224i | \(-0.972169\pi\) | ||||
−0.996180 | + | 0.0873224i | \(0.972169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.610051 | −0.157515 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.302704 | 0.0734165 | 0.0367082 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367082 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.60244 | −1.28529 | −0.642644 | − | 0.766165i | \(-0.722163\pi\) | ||||
−0.642644 | + | 0.766165i | \(0.722163\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.27841 | 0.278973 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77229 | −0.954457 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.58112 | −1.07409 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0166785 | 0.00309712 | 0.00154856 | − | 0.999999i | \(-0.499507\pi\) | ||||
0.00154856 | + | 0.999999i | \(0.499507\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.66075 | 1.37591 | 0.687956 | − | 0.725753i | \(-0.258508\pi\) | ||||
0.687956 | + | 0.725753i | \(0.258508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.11365 | −0.542018 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.477194 | −0.0806605 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.93916 | −1.46959 | −0.734795 | − | 0.678289i | \(-0.762722\pi\) | ||||
−0.734795 | + | 0.678289i | \(0.762722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.18356 | −1.47055 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6115 | 1.65724 | 0.828619 | − | 0.559812i | \(-0.189127\pi\) | ||||
0.828619 | + | 0.559812i | \(0.189127\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.03039 | 0.767127 | 0.383564 | − | 0.923514i | \(-0.374697\pi\) | ||||
0.383564 | + | 0.923514i | \(0.374697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.651684 | 0.0971473 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.27841 | −0.478206 | −0.239103 | − | 0.970994i | \(-0.576853\pi\) | ||||
−0.239103 | + | 0.970994i | \(0.576853\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.386981 | 0.0541881 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.11365 | 0.427693 | 0.213847 | − | 0.976867i | \(-0.431401\pi\) | ||||
0.213847 | + | 0.976867i | \(0.431401\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16223 | 0.156716 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.16223 | −0.948661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.90514 | −1.02916 | −0.514581 | − | 0.857442i | \(-0.672053\pi\) | ||||
−0.514581 | + | 0.857442i | \(0.672053\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.4620 | 1.33952 | 0.669759 | − | 0.742579i | \(-0.266397\pi\) | ||||
0.669759 | + | 0.742579i | \(0.266397\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.36566 | −0.172057 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.42795 | 0.425185 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.78454 | −0.340186 | −0.170093 | − | 0.985428i | \(-0.554407\pi\) | ||||
−0.170093 | + | 0.985428i | \(0.554407\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.27841 | −0.153903 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.641953 | −0.0761858 | −0.0380929 | − | 0.999274i | \(-0.512128\pi\) | ||||
−0.0380929 | + | 0.999274i | \(0.512128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.3124 | 1.20698 | 0.603490 | − | 0.797371i | \(-0.293776\pi\) | ||||
0.603490 | + | 0.797371i | \(0.293776\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.10096 | −0.704478 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.43556 | −0.277558 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.43556 | 0.274022 | 0.137011 | − | 0.990570i | \(-0.456250\pi\) | ||||
0.137011 | + | 0.990570i | \(0.456250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.03800 | −0.337556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.7343 | −1.28801 | −0.644003 | − | 0.765023i | \(-0.722727\pi\) | ||||
−0.644003 | + | 0.765023i | \(0.722727\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.144448 | −0.0156676 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.0213220 | 0.00228596 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.59085 | −0.804628 | −0.402314 | − | 0.915502i | \(-0.631794\pi\) | ||||
−0.402314 | + | 0.915502i | \(0.631794\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.18356 | −0.753041 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.79361 | 1.01555 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.67345 | 0.274290 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.12525 | −0.114251 | −0.0571257 | − | 0.998367i | \(-0.518194\pi\) | ||||
−0.0571257 | + | 0.998367i | \(0.518194\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.32615 | 0.334290 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.46131 | −0.941435 | −0.470718 | − | 0.882284i | \(-0.656005\pi\) | ||||
−0.470718 | + | 0.882284i | \(0.656005\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.348980 | 0.0343860 | 0.0171930 | − | 0.999852i | \(-0.494527\pi\) | ||||
0.0171930 | + | 0.999852i | \(0.494527\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.610051 | −0.0595349 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.223070 | −0.0215650 | −0.0107825 | − | 0.999942i | \(-0.503432\pi\) | ||||
−0.0107825 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5264 | 1.58294 | 0.791470 | − | 0.611208i | \(-0.209316\pi\) | ||||
0.791470 | + | 0.611208i | \(0.209316\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.4279 | −1.08469 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0181 | −1.50686 | −0.753430 | − | 0.657529i | \(-0.771602\pi\) | ||||
−0.753430 | + | 0.657529i | \(0.771602\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.477194 | 0.0444986 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.81029 | 0.906961 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.302704 | 0.0277488 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.06804 | −0.460731 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5659 | 1.22320 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.66328 | 0.417096 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0699024 | −0.00620284 | −0.00310142 | − | 0.999995i | \(-0.500987\pi\) | ||||
−0.00310142 | + | 0.999995i | \(0.500987\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.43092 | 0.566211 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.14954 | −0.712028 | −0.356014 | − | 0.934481i | \(-0.615865\pi\) | ||||
−0.356014 | + | 0.934481i | \(0.615865\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.60244 | −0.485793 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66328 | 0.229218 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −9.42795 | −0.805484 | −0.402742 | − | 0.915314i | \(-0.631943\pi\) | ||||
−0.402742 | + | 0.915314i | \(0.631943\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5209 | −1.14683 | −0.573416 | − | 0.819264i | \(-0.694382\pi\) | ||||
−0.573416 | + | 0.819264i | \(0.694382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.19117 | −0.352960 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.4960 | 1.46309 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.00795888 | −0.000660949 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.27841 | 0.105442 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.4157 | 1.18098 | 0.590490 | − | 0.807045i | \(-0.298935\pi\) | ||||
0.590490 | + | 0.807045i | \(0.298935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.418883 | 0.0340882 | 0.0170441 | − | 0.999855i | \(-0.494574\pi\) | ||||
0.0170441 | + | 0.999855i | \(0.494574\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.413390 | −0.0334206 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.65566 | −0.293630 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 24.3555 | 1.94378 | 0.971891 | − | 0.235431i | \(-0.0756500\pi\) | ||||
0.971891 | + | 0.235431i | \(0.0756500\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.98054 | 0.315677 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.18653 | 0.327914 | 0.163957 | − | 0.986467i | \(-0.447574\pi\) | ||||
0.163957 | + | 0.986467i | \(0.447574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.48582 | 0.115671 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5756 | −1.05051 | −0.525257 | − | 0.850944i | \(-0.676031\pi\) | ||||
−0.525257 | + | 0.850944i | \(0.676031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 38.6035 | 2.96950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.65102 | 0.585088 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.5293 | 1.18067 | 0.590337 | − | 0.807157i | \(-0.298995\pi\) | ||||
0.590337 | + | 0.807157i | \(0.298995\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.77229 | −0.360751 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1060 | −0.759617 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.5550 | −1.53635 | −0.768175 | − | 0.640240i | \(-0.778835\pi\) | ||||
−0.768175 | + | 0.640240i | \(0.778835\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.06441 | −0.450764 | −0.225382 | − | 0.974270i | \(-0.572363\pi\) | ||||
−0.225382 | + | 0.974270i | \(0.572363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3747 | 0.988688 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.26571 | 0.313622 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.737254 | −0.0539133 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.58112 | −0.405967 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2838 | −1.03354 | −0.516771 | − | 0.856123i | \(-0.672866\pi\) | ||||
−0.516771 | + | 0.856123i | \(0.672866\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4037 | 0.892835 | 0.446417 | − | 0.894825i | \(-0.352700\pi\) | ||||
0.446417 | + | 0.894825i | \(0.352700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.38234 | 0.313826 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6420 | −0.758208 | −0.379104 | − | 0.925354i | \(-0.623768\pi\) | ||||
−0.379104 | + | 0.925354i | \(0.623768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1318 | −0.789112 | −0.394556 | − | 0.918872i | \(-0.629102\pi\) | ||||
−0.394556 | + | 0.918872i | \(0.629102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.55980 | −0.251089 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0166785 | 0.00117060 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.06375 | −0.353667 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.36566 | 0.0949198 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.6451 | 0.943850 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.3489 | −1.74509 | −0.872546 | − | 0.488532i | \(-0.837532\pi\) | ||||
−0.872546 | + | 0.488532i | \(0.837532\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.820682 | −0.0562322 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.40047 | −0.163711 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.66075 | 0.520046 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.1836 | 0.890862 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.17449 | −0.146272 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.45900 | 0.231632 | 0.115816 | − | 0.993271i | \(-0.463052\pi\) | ||||
0.115816 | + | 0.993271i | \(0.463052\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.51731 | 0.434488 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.24253 | −0.281587 | −0.140793 | − | 0.990039i | \(-0.544965\pi\) | ||||
−0.140793 | + | 0.990039i | \(0.544965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0978 | −0.931607 | −0.465803 | − | 0.884888i | \(-0.654235\pi\) | ||||
−0.465803 | + | 0.884888i | \(0.654235\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.11365 | −0.204863 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −29.0239 | −1.90142 | −0.950709 | − | 0.310085i | \(-0.899643\pi\) | ||||
−0.950709 | + | 0.310085i | \(0.899643\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.56444 | 0.102053 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.11365 | 0.202254 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.5507 | −1.26463 | −0.632314 | − | 0.774712i | \(-0.717895\pi\) | ||||
−0.632314 | + | 0.774712i | \(0.717895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.6031 | 0.683006 | 0.341503 | − | 0.939881i | \(-0.389064\pi\) | ||||
0.341503 | + | 0.939881i | \(0.389064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.8595 | 0.824939 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.477194 | −0.0304868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.2454 | 2.56076 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.0013 | −0.950667 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.4765 | 1.92366 | 0.961829 | − | 0.273651i | \(-0.0882315\pi\) | ||||
0.961829 | + | 0.273651i | \(0.0882315\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.43556 | 0.153122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.184665 | −0.0115642 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6339 | 0.850462 | 0.425231 | − | 0.905085i | \(-0.360193\pi\) | ||||
0.425231 | + | 0.905085i | \(0.360193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.93916 | −0.555453 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0227771 | −0.00140987 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.64044 | −0.594455 | −0.297227 | − | 0.954807i | \(-0.596062\pi\) | ||||
−0.297227 | + | 0.954807i | \(0.596062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.48582 | −0.0912730 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.70424 | −0.593890 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.6766 | 1.56553 | 0.782764 | − | 0.622318i | \(-0.213809\pi\) | ||||
0.782764 | + | 0.622318i | \(0.213809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.4801 | 1.24408 | 0.622039 | − | 0.782986i | \(-0.286305\pi\) | ||||
0.622039 | + | 0.782986i | \(0.286305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −9.18356 | −0.555814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.6232 | 0.700905 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.65247 | 0.0992876 | 0.0496438 | − | 0.998767i | \(-0.484191\pi\) | ||||
0.0496438 | + | 0.998767i | \(0.484191\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.4620 | −0.626342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.35195 | −0.319270 | −0.159635 | − | 0.987176i | \(-0.551032\pi\) | ||||
−0.159635 | + | 0.987176i | \(0.551032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.731317 | −0.0434723 | −0.0217362 | − | 0.999764i | \(-0.506919\pi\) | ||||
−0.0217362 | + | 0.999764i | \(0.506919\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.41777 | 0.202451 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6115 | 0.626377 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9084 | −0.994610 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.43853 | −0.0843281 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.2528 | −0.598975 | −0.299487 | − | 0.954100i | \(-0.596816\pi\) | ||||
−0.299487 | + | 0.954100i | \(0.596816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.77229 | 0.219631 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.5932 | 0.788755 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.18356 | 0.415436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.03039 | 0.289947 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.0955 | −0.694866 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.99239 | −0.285863 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9841 | −0.969335 | −0.484667 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484667 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.446141 | 0.0253801 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.05831 | 0.456945 | 0.228472 | − | 0.973550i | \(-0.426627\pi\) | ||||
0.228472 | + | 0.973550i | \(0.426627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.68801 | −0.208459 | −0.104229 | − | 0.994553i | \(-0.533238\pi\) | ||||
−0.104229 | + | 0.994553i | \(0.533238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.651684 | 0.0367182 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.30965 | −0.242054 | −0.121027 | − | 0.992649i | \(-0.538619\pi\) | ||||
−0.121027 | + | 0.992649i | \(0.538619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0406215 | −0.00227437 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.285176 | −0.0159170 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.69588 | −0.0943613 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.2820 | 1.90162 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.1275 | 1.16836 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.27841 | −0.180745 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.0285 | 1.48562 | 0.742811 | − | 0.669501i | \(-0.233492\pi\) | ||||
0.742811 | + | 0.669501i | \(0.233492\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.2078 | 0.668986 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.32877 | 0.0725982 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.50395 | −0.517713 | −0.258857 | − | 0.965916i | \(-0.583346\pi\) | ||||
−0.258857 | + | 0.965916i | \(0.583346\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.4778 | −1.11220 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.6582 | −1.01040 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.610051 | 0.0328440 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.8863 | −1.06755 | −0.533776 | − | 0.845626i | \(-0.679227\pi\) | ||||
−0.533776 | + | 0.845626i | \(0.679227\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.91064 | 0.102274 | 0.0511370 | − | 0.998692i | \(-0.483715\pi\) | ||||
0.0511370 | + | 0.998692i | \(0.483715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40.0923 | 2.13997 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.4109 | 1.35248 | 0.676242 | − | 0.736680i | \(-0.263607\pi\) | ||||
0.676242 | + | 0.736680i | \(0.263607\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.306336 | 0.0162586 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.386981 | 0.0204812 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.9497 | 1.79180 | 0.895898 | − | 0.444260i | \(-0.146533\pi\) | ||||
0.895898 | + | 0.444260i | \(0.146533\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3873 | 0.651965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.47905 | −0.340062 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.92103 | −0.257579 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.2577 | 1.84044 | 0.920218 | − | 0.391405i | \(-0.128011\pi\) | ||||
0.920218 | + | 0.391405i | \(0.128011\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.4917 | −0.754408 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.11365 | 0.161653 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.4381 | 1.11002 | 0.555012 | − | 0.831842i | \(-0.312714\pi\) | ||||
0.555012 | + | 0.831842i | \(0.312714\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.96159 | 0.307855 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.119811 | −0.00617058 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.5754 | −0.748686 | −0.374343 | − | 0.927290i | \(-0.622132\pi\) | ||||
−0.374343 | + | 0.927290i | \(0.622132\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.0893642 | −0.00457827 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.9999 | 1.48183 | 0.740914 | − | 0.671600i | \(-0.234393\pi\) | ||||
0.740914 | + | 0.671600i | \(0.234393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.16223 | 0.0592330 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.86979 | −0.349211 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.72336 | 0.239484 | 0.119742 | − | 0.992805i | \(-0.461793\pi\) | ||||
0.119742 | + | 0.992805i | \(0.461793\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.302704 | −0.0153084 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.4185 | −0.525543 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.16223 | −0.0584784 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.2972 | −1.62095 | −0.810475 | − | 0.585773i | \(-0.800791\pi\) | ||||
−0.810475 | + | 0.585773i | \(0.800791\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.16223 | −0.358560 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6054 | 1.12886 | 0.564430 | − | 0.825481i | \(-0.309096\pi\) | ||||
0.564430 | + | 0.825481i | \(0.309096\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −55.0314 | −2.74131 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.44972 | 0.0720369 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7719 | 1.07919 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2097 | −0.504838 | −0.252419 | − | 0.967618i | \(-0.581226\pi\) | ||||
−0.252419 | + | 0.967618i | \(0.581226\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.0528 | −0.594522 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.90514 | −0.388987 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.59953 | 0.274870 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.2854 | −0.846468 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.2273 | 0.890462 | 0.445231 | − | 0.895416i | \(-0.353122\pi\) | ||||
0.445231 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.15630 | −0.153829 | −0.0769143 | − | 0.997038i | \(-0.524507\pi\) | ||||
−0.0769143 | + | 0.997038i | \(0.524507\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.47719 | 0.217689 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.44459 | −0.0700729 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.4620 | 0.506290 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.3671 | 1.07989 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.39326 | −0.259784 | −0.129892 | − | 0.991528i | \(-0.541463\pi\) | ||||
−0.129892 | + | 0.991528i | \(0.541463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.39526 | 0.307336 | 0.153668 | − | 0.988123i | \(-0.450891\pi\) | ||||
0.153668 | + | 0.988123i | \(0.450891\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.0101747 | −0.000487842 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.60244 | 0.268001 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −37.1943 | −1.77519 | −0.887594 | − | 0.460626i | \(-0.847625\pi\) | ||||
−0.887594 | + | 0.460626i | \(0.847625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.36566 | −0.0650314 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.2228 | −1.72100 | −0.860498 | − | 0.509453i | \(-0.829848\pi\) | ||||
−0.860498 | + | 0.509453i | \(0.829848\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.62231 | 0.171714 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.4292 | 0.871672 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.8859 | −1.45760 | −0.728799 | − | 0.684728i | \(-0.759921\pi\) | ||||
−0.728799 | + | 0.684728i | \(0.759921\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −25.8450 | −1.21699 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.535505 | 0.0251602 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.42795 | 0.160705 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.2852 | −0.668232 | −0.334116 | − | 0.942532i | \(-0.608438\pi\) | ||||
−0.334116 | + | 0.942532i | \(0.608438\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.68943 | −0.0788556 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.40069 | −0.437834 | −0.218917 | − | 0.975744i | \(-0.570252\pi\) | ||||
−0.218917 | + | 0.975744i | \(0.570252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.9015 | 1.01785 | 0.508925 | − | 0.860811i | \(-0.330043\pi\) | ||||
0.508925 | + | 0.860811i | \(0.330043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.67345 | −0.216726 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.9877 | 1.38766 | 0.693832 | − | 0.720137i | \(-0.255921\pi\) | ||||
0.693832 | + | 0.720137i | \(0.255921\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.78454 | −0.128578 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.1364 | 1.43469 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.2518 | −0.563339 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.7364 | 1.22675 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.25219 | −0.194694 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.24253 | 0.193846 | 0.0969231 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969231 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 64.2150 | 2.92795 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.27841 | −0.0581698 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.536960 | 0.0243821 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.96478 | −0.270290 | −0.135145 | − | 0.990826i | \(-0.543150\pi\) | ||||
−0.135145 | + | 0.990826i | \(0.543150\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.35211 | 0.242031 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.20175 | 0.279881 | 0.139940 | − | 0.990160i | \(-0.455309\pi\) | ||||
0.139940 | + | 0.990160i | \(0.455309\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.00504865 | 0.000227380 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.58722 | −0.0713401 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.641953 | −0.0287955 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.6753 | 0.791253 | 0.395626 | − | 0.918412i | \(-0.370527\pi\) | ||||
0.395626 | + | 0.918412i | \(0.370527\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.3553 | −0.775376 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.1635 | −1.52328 | −0.761638 | − | 0.648003i | \(-0.775604\pi\) | ||||
−0.761638 | + | 0.648003i | \(0.775604\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.51488 | 0.200909 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.3512 | 2.19176 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.4383 | −0.817265 | −0.408633 | − | 0.912699i | \(-0.633994\pi\) | ||||
−0.408633 | + | 0.912699i | \(0.633994\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.3124 | 0.456195 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.2679 | 1.38051 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.166531 | −0.00733824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.98478 | 0.351170 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.8529 | 0.871447 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8840 | −0.520647 | −0.260323 | − | 0.965521i | \(-0.583829\pi\) | ||||
−0.260323 | + | 0.965521i | \(0.583829\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8711 | −0.562815 | −0.281407 | − | 0.959588i | \(-0.590801\pi\) | ||||
−0.281407 | + | 0.959588i | \(0.590801\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.10096 | −0.266268 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.31894 | 0.101015 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7957 | 0.468495 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −76.2284 | −3.30182 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.106448 | 0.00460214 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −26.2777 | −1.13397 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.43556 | −0.104907 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −30.3533 | −1.30499 | −0.652496 | − | 0.757792i | \(-0.726278\pi\) | ||||
−0.652496 | + | 0.757792i | \(0.726278\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.75282 | −0.332706 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.88629 | −0.337811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.2001 | −1.46229 | −0.731144 | − | 0.682223i | \(-0.761013\pi\) | ||||
−0.731144 | + | 0.682223i | \(0.761013\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.2875 | −0.609775 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0934403 | −0.00398069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.43556 | 0.103571 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.45335 | 0.231482 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.2289 | −1.23847 | −0.619235 | − | 0.785206i | \(-0.712557\pi\) | ||||
−0.619235 | + | 0.785206i | \(0.712557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.1361 | −1.52839 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.942515 | −0.0397930 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4170 | 0.986907 | 0.493454 | − | 0.869772i | \(-0.335734\pi\) | ||||
0.493454 | + | 0.869772i | \(0.335734\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.64376 | 0.321575 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.03800 | −0.127584 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.8255 | −1.33419 | −0.667097 | − | 0.744971i | \(-0.732464\pi\) | ||||
−0.667097 | + | 0.744971i | \(0.732464\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8639 | 0.538336 | 0.269168 | − | 0.963093i | \(-0.413251\pi\) | ||||
0.269168 | + | 0.963093i | \(0.413251\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.2607 | −0.762850 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.77229 | 0.199018 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.25457 | −0.177120 | −0.0885600 | − | 0.996071i | \(-0.528226\pi\) | ||||
−0.0885600 | + | 0.996071i | \(0.528226\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.8570 | 0.658995 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.7343 | −0.486820 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.58350 | −0.314076 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.68141 | −0.193552 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.9185 | −1.15232 | −0.576160 | − | 0.817337i | \(-0.695450\pi\) | ||||
−0.576160 | + | 0.817337i | \(0.695450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42.9189 | −1.76844 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.6048 | −0.559627 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.8711 | −0.774944 | −0.387472 | − | 0.921881i | \(-0.626652\pi\) | ||||
−0.387472 | + | 0.921881i | \(0.626652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.144448 | −0.00592181 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.2310 | −0.582437 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.56833 | −0.186657 | −0.0933285 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933285 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.16113 | 0.332899 | 0.166450 | − | 0.986050i | \(-0.446770\pi\) | ||||
0.166450 | + | 0.986050i | \(0.446770\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.80273 | 0.154859 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.41844 | 0.0983235 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3331 | 0.703529 | 0.351764 | − | 0.936089i | \(-0.385582\pi\) | ||||
0.351764 | + | 0.936089i | \(0.385582\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0213220 | 0.000864012 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.5507 | 0.952758 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5952 | 0.468325 | 0.234162 | − | 0.972198i | \(-0.424765\pi\) | ||||
0.234162 | + | 0.972198i | \(0.424765\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.47356 | −0.261039 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6206 | −0.508087 | −0.254044 | − | 0.967193i | \(-0.581761\pi\) | ||||
−0.254044 | + | 0.967193i | \(0.581761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.3244 | −1.41981 | −0.709904 | − | 0.704298i | \(-0.751262\pi\) | ||||
−0.709904 | + | 0.704298i | \(0.751262\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.58112 | 0.223963 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.59085 | −0.304121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.6361 | 0.865446 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.4441 | 0.696649 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.70592 | −0.107892 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.5356 | −0.419417 | −0.209708 | − | 0.977764i | \(-0.567251\pi\) | ||||
−0.209708 | + | 0.977764i | \(0.567251\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.4064 | −1.28804 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0333570 | 0.00132373 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.18356 | −0.284623 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.876689 | 0.0346813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.8906 | 0.904124 | 0.452062 | − | 0.891987i | \(-0.350689\pi\) | ||||
0.452062 | + | 0.891987i | \(0.350689\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.8893 | −0.902664 | −0.451332 | − | 0.892356i | \(-0.649051\pi\) | ||||
−0.451332 | + | 0.892356i | \(0.649051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.06879 | −0.120834 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.5209 | −1.43578 | −0.717892 | − | 0.696154i | \(-0.754893\pi\) | ||||
−0.717892 | + | 0.696154i | \(0.754893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.2535 | 0.755764 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.79361 | 0.383842 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4493 | −0.604577 | −0.302288 | − | 0.953217i | \(-0.597751\pi\) | ||||
−0.302288 | + | 0.953217i | \(0.597751\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.88891 | 0.151952 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0833 | −0.549441 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.1664 | −1.79839 | −0.899194 | − | 0.437550i | \(-0.855846\pi\) | ||||
−0.899194 | + | 0.437550i | \(0.855846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.6047 | 1.50155 | 0.750774 | − | 0.660559i | \(-0.229681\pi\) | ||||
0.750774 | + | 0.660559i | \(0.229681\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.77990 | −0.107962 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.67345 | 0.103672 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0166785 | −0.000645794 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.42204 | 0.170966 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.4808 | −0.983674 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7906 | −0.647232 | −0.323616 | − | 0.946189i | \(-0.604899\pi\) | ||||
−0.323616 | + | 0.946189i | \(0.604899\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 26.6347 | 1.02517 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.7560 | 1.10518 | 0.552591 | − | 0.833452i | \(-0.313639\pi\) | ||||
0.552591 | + | 0.833452i | \(0.313639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.12525 | −0.0431830 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.42371 | −0.207837 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.1501 | 0.388384 | 0.194192 | − | 0.980964i | \(-0.437791\pi\) | ||||
0.194192 | + | 0.980964i | \(0.437791\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.49896 | 0.171896 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.0228 | −0.687612 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.3671 | −0.852119 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.33903 | −0.127023 | −0.0635113 | − | 0.997981i | \(-0.520230\pi\) | ||||
−0.0635113 | + | 0.997981i | \(0.520230\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.32615 | 0.126350 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.45211 | 0.244743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.21214 | 0.121669 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −37.1045 | −1.40342 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.3756 | −1.33612 | −0.668060 | − | 0.744107i | \(-0.732875\pi\) | ||||
−0.668060 | + | 0.744107i | \(0.732875\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.0811 | 1.88885 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.00000 | 0.0753244 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.46131 | −0.355829 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.7761 | 1.56894 | 0.784468 | − | 0.620170i | \(-0.212936\pi\) | ||||
0.784468 | + | 0.620170i | \(0.212936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.32615 | −0.124740 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.66075 | −0.286897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.34898 | −0.312234 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9938 | −0.933412 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.24913 | 0.121172 | 0.0605861 | − | 0.998163i | \(-0.480703\pi\) | ||||
0.0605861 | + | 0.998163i | \(0.480703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.348980 | 0.0129967 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.5552 | 0.504122 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0795946 | −0.00295607 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.63289 | −0.357264 | −0.178632 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178632 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.5538 | 0.946437 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.52272 | 0.0563198 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.8899 | 1.25175 | 0.625876 | − | 0.779922i | \(-0.284741\pi\) | ||||
0.625876 | + | 0.779922i | \(0.284741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.610051 | −0.0225021 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.78192 | 0.249815 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.3805 | −1.26471 | −0.632353 | − | 0.774680i | \(-0.717911\pi\) | ||||
−0.632353 | + | 0.774680i | \(0.717911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 51.4503 | 1.89007 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.2805 | −0.890766 | −0.445383 | − | 0.895340i | \(-0.646933\pi\) | ||||
−0.445383 | + | 0.895340i | \(0.646933\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.87908 | −0.252030 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.0250 | 0.586325 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.223070 | −0.00815082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.6514 | 0.826560 | 0.413280 | − | 0.910604i | \(-0.364383\pi\) | ||||
0.413280 | + | 0.910604i | \(0.364383\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.9615 | 1.41984 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.199888 | −0.00727468 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0528 | −0.801523 | −0.400762 | − | 0.916182i | \(-0.631254\pi\) | ||||
−0.400762 | + | 0.916182i | \(0.631254\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.11365 | 0.113018 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.9416 | 0.577883 | 0.288941 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288941 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.5264 | 0.598295 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.197267 | 0.00713221 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.7870 | 2.05046 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.4438 | 1.42238 | 0.711190 | − | 0.703000i | \(-0.248157\pi\) | ||||
0.711190 | + | 0.703000i | \(0.248157\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.4298 | 0.627719 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.0375 | −1.51198 | −0.755992 | − | 0.654581i | \(-0.772845\pi\) | ||||
−0.755992 | + | 0.654581i | \(0.772845\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.5593 | −1.31325 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.4279 | −0.409975 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −59.4503 | −2.13003 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.56352 | 0.0559470 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.0930847 | −0.00332658 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.6223 | −0.414818 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.98472 | −0.248978 | −0.124489 | − | 0.992221i | \(-0.539729\pi\) | ||||
−0.124489 | + | 0.992221i | \(0.539729\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.3245 | −0.438763 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.0181 | −0.569539 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −75.1542 | −2.66880 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.89949 | −0.0673679 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.2541 | 0.929969 | 0.464984 | − | 0.885319i | \(-0.346060\pi\) | ||||
0.464984 | + | 0.885319i | \(0.346060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.992388 | −0.0351082 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.3665 | 0.366283 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.1166 | −0.886344 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.477194 | 0.0168189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 32.8253 | 1.15550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.30337 | 0.116140 | 0.0580701 | − | 0.998313i | \(-0.481505\pi\) | ||||
0.0580701 | + | 0.998313i | \(0.481505\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.5817 | −1.03875 | −0.519377 | − | 0.854545i | \(-0.673836\pi\) | ||||
−0.519377 | + | 0.854545i | \(0.673836\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.1820 | 0.918244 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.99778 | −0.0699793 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.1824 | −0.985979 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9.81029 | 0.342799 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.4549 | −1.90049 | −0.950245 | − | 0.311504i | \(-0.899167\pi\) | ||||
−0.950245 | + | 0.311504i | \(0.899167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.7484 | −0.444381 | −0.222191 | − | 0.975003i | \(-0.571321\pi\) | ||||
−0.222191 | + | 0.975003i | \(0.571321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.8592 | 0.517333 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.2940 | 0.775239 | 0.387620 | − | 0.921819i | \(-0.373297\pi\) | ||||
0.387620 | + | 0.921819i | \(0.373297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.25845 | −0.0784392 | −0.0392196 | − | 0.999231i | \(-0.512487\pi\) | ||||
−0.0392196 | + | 0.999231i | \(0.512487\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.11255 | 0.0732834 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.302704 | 0.0104881 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.47821 | 0.224188 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.7555 | −1.47785 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.8393 | 1.34088 | 0.670442 | − | 0.741962i | \(-0.266105\pi\) | ||||
0.670442 | + | 0.741962i | \(0.266105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9997 | −0.999990 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.84200 | −0.235651 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.4213 | −0.633714 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.06804 | −0.174140 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.934926 | −0.0320866 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.93916 | 0.306431 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.34045 | 0.114375 | 0.0571873 | − | 0.998363i | \(-0.481787\pi\) | ||||
0.0571873 | + | 0.998363i | \(0.481787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.65102 | −0.124862 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.3153 | 1.20635 | 0.603174 | − | 0.797610i | \(-0.293903\pi\) | ||||
0.603174 | + | 0.797610i | \(0.293903\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.5433 | 1.28096 | 0.640481 | − | 0.767974i | \(-0.278735\pi\) | ||||
0.640481 | + | 0.767974i | \(0.278735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.5659 | 0.462324 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.1921 | −1.09583 | −0.547916 | − | 0.836534i | \(-0.684579\pi\) | ||||
−0.547916 | + | 0.836534i | \(0.684579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.41051 | −0.251965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.6159 | −0.734114 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.93196 | −0.201228 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.0029 | 0.677773 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.53670 | 0.0520095 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.66328 | 0.157647 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.78157 | −0.330300 | −0.165150 | − | 0.986268i | \(-0.552811\pi\) | ||||
−0.165150 | + | 0.986268i | \(0.552811\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −13.1073 | −0.442099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.3634 | 1.46095 | 0.730475 | − | 0.682939i | \(-0.239299\pi\) | ||||
0.730475 | + | 0.682939i | \(0.239299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.7422 | 1.57300 | 0.786500 | − | 0.617590i | \(-0.211891\pi\) | ||||
0.786500 | + | 0.617590i | \(0.211891\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.82254 | 0.162108 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.5913 | −1.29577 | −0.647885 | − | 0.761738i | \(-0.724346\pi\) | ||||
−0.647885 | + | 0.761738i | \(0.724346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0699024 | −0.00234445 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.39924 | 0.247884 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 18.3671 | 0.614632 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.80870 | 0.327869 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.18356 | 0.306630 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.127770 | 0.00426136 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.942515 | 0.0313997 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.43092 | 0.214008 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.89390 | 0.0961965 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.5641 | −0.616411 | −0.308205 | − | 0.951320i | \(-0.599728\pi\) | ||||
−0.308205 | + | 0.951320i | \(0.599728\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.9209 | 0.428560 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.69995 | −0.155716 | −0.0778581 | − | 0.996964i | \(-0.524808\pi\) | ||||
−0.0778581 | + | 0.996964i | \(0.524808\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.5796 | 0.945846 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.38234 | −0.210994 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.14954 | −0.269121 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43.7947 | −1.44465 | −0.722326 | − | 0.691552i | \(-0.756927\pi\) | ||||
−0.722326 | + | 0.691552i | \(0.756927\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.7127 | −0.715458 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.61151 | 0.151790 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.6602 | 1.40266 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.476588 | −0.0156532 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27.4615 | 0.900982 | 0.450491 | − | 0.892781i | \(-0.351249\pi\) | ||||
0.450491 | + | 0.892781i | \(0.351249\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.60244 | −0.183613 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10.3019 | 0.337268 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.351813 | 0.0115055 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.5337 | −0.866819 | −0.433410 | − | 0.901197i | \(-0.642690\pi\) | ||||
−0.433410 | + | 0.901197i | \(0.642690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.71480 | −0.153862 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.5366 | 1.77784 | 0.888922 | − | 0.458059i | \(-0.151455\pi\) | ||||
0.888922 | + | 0.458059i | \(0.151455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6115 | −0.345558 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.66328 | 0.0866363 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.3392 | −0.530951 | −0.265476 | − | 0.964118i | \(-0.585529\pi\) | ||||
−0.265476 | + | 0.964118i | \(0.585529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −74.0800 | −2.40474 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.50952 | −0.178658 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.02906 | −0.162907 | −0.0814536 | − | 0.996677i | \(-0.525956\pi\) | ||||
−0.0814536 | + | 0.996677i | \(0.525956\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.81616 | 0.220566 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.0519311 | −0.00167869 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.42795 | −0.304444 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.6871 | 0.893132 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.304638 | 0.00981683 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.91895 | −0.190538 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.4970 | 1.78466 | 0.892332 | − | 0.451379i | \(-0.149068\pi\) | ||||
0.892332 | + | 0.451379i | \(0.149068\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.16804 | −0.0696473 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53.3518 | 1.71214 | 0.856071 | − | 0.516858i | \(-0.172899\pi\) | ||||
0.856071 | + | 0.516858i | \(0.172899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.5209 | −0.433462 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 43.8266 | 1.40357 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.0073 | 0.320161 | 0.160080 | − | 0.987104i | \(-0.448825\pi\) | ||||
0.160080 | + | 0.987104i | \(0.448825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.4880 | 0.590878 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22.5694 | −0.720585 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.7241 | −0.533414 | −0.266707 | − | 0.963778i | \(-0.585936\pi\) | ||||
−0.266707 | + | 0.963778i | \(0.585936\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.07827 | 0.161807 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.19117 | −0.133406 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.03039 | −0.159957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.96165 | 0.284676 | 0.142338 | − | 0.989818i | \(-0.454538\pi\) | ||||
0.142338 | + | 0.989818i | \(0.454538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.5536 | 1.09653 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.31202 | 0.168402 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7263 | 0.371376 | 0.185688 | − | 0.982609i | \(-0.440549\pi\) | ||||
0.185688 | + | 0.982609i | \(0.440549\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 49.8905 | 1.57847 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1288.2.a.n.1.4 | ✓ | 4 | |
4.3 | odd | 2 | 2576.2.a.ba.1.1 | 4 | |||
7.6 | odd | 2 | 9016.2.a.bf.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1288.2.a.n.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
2576.2.a.ba.1.1 | 4 | 4.3 | odd | 2 | |||
9016.2.a.bf.1.1 | 4 | 7.6 | odd | 2 |